Extending the number system

Practice sheet

Fresh questions from the whole chapter, to do on paper.

New questions

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  1. Evaluate 365236^{ \frac{ 5 }{2} }.
  2. Evaluate 125−23125^{ -\frac{ 2 }{3} }.
  3. Which number is irrational?
    1. 2\sqrt{ 2 }
    2. 4\sqrt{ 4 }
    3. 0.1‾0.\overline{ 1 }
  4. Write 0.1‾0.\overline{ 1 } (the digit 1 repeating forever) as a fraction.
  5. Write 0.48‾0.\overline{ 48 } (the digits 48 repeating forever) as a fraction.
  6. Write −121\sqrt{-121} in terms of ii.
  7. Simplify i10i^{ 10 }.
  8. Which number is real?
    1. (9i)2(9i)^2
    2. −9\sqrt{-9}
    3. 9+i9 + i
  9. Add: (9+8i)+(2+1i)(9 + 8i) + (2 + 1i).
  10. Multiply: (2+8i)(2−8i)(2 + 8i)(2 - 8i).
  11. Expand (3+6i)2(3 + 6i)^2.
  12. Expand (x+6)(x+9)(x + 6)(x + 9). What is the coefficient of xx?

Answers

  1. 77767776
  2. 125\frac{1}{25}
  3. 2\sqrt{ 2 }
  4. 19\frac{1}{9}
  5. 1633\frac{16}{33}
  6. 11i11 i
  7. −1-1
  8. (9i)2(9i)^2
  9. 11+9i11 + 9 i
  10. 6868
  11. −27+36i-27 + 36 i
  12. 1515